Question
In the triangle ABC given, side AB is twice as long as side AC. We have:
m<BAC=120°
mBC= 8cm
Determine rounded to the nearest unit, the perimeter of triangle ABC.
m<BAC=120°
mBC= 8cm
Determine rounded to the nearest unit, the perimeter of triangle ABC.
Answers
Reiny
Let AC = x
let AB = 2x
We can use the cosine law to find x
x^2 + (2x)^2 - 2(x)(2x)cos120° = 8^2
5x^2 - 4x^2(-1/2) = 64
7x^2 = 64
x^2 = 64/7
x = 8/√7
perimeter = x+2x+8
= 3x + 8
= 24/√7 + 8 = appr 17
let AB = 2x
We can use the cosine law to find x
x^2 + (2x)^2 - 2(x)(2x)cos120° = 8^2
5x^2 - 4x^2(-1/2) = 64
7x^2 = 64
x^2 = 64/7
x = 8/√7
perimeter = x+2x+8
= 3x + 8
= 24/√7 + 8 = appr 17